The algebra \({M}{}\)  is not commutative in general and the space \((M)\)  is not an algebra. This poses a direct issue for a straightforward generalization of the Gelfand representation and Belishev's 2-dimensional boundary control method [1]}, but it does not thwart the effort completely since Belishev and Vakulenko manage to build a 3-dimensional version [2]}. Extending this approach, we will use insight on axial fields from those two authors but make the change to think not of an axis, but of a plane. Of course, in \(^3\)  a plane and axis are dual, but when we extend beyond dimension-3, we will be required to use planes. If \(S\)  is dimension 2, then \(^{+}(S)\)  is a copy of the commutative algebra of holomorphic functions. Intuitively, we can build commutative Banach algebras of monogenic fields for surfaces in \(M\) .
